I'm studying QFT and am confused on the field strength tensor for some quantum field. I've seen the tensor written as the commutator of the covariant derivative $$-igF_{\mu\nu}=[D_\mu, D_\nu].$$ Is this just a defined quantity that happens to give the lagrangian when summed over, or is there something deeper behind it?
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$\begingroup$ Possible duplicate: physics.stackexchange.com/q/182612/2451 $\endgroup$– Qmechanic ♦Commented Aug 19, 2022 at 14:15
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$\begingroup$ It just means that $F$ is the curvature of the gauge field. $\endgroup$– Jeanbaptiste RouxCommented Aug 19, 2022 at 14:40
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